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Comments

Don't make a noise is a COMMAND. You can't tell people what to do in the PAST.

The verb in a clause introduced by while is chosen on ordinary grounds. The word while doesn't make any difference.

Unlike some languages, English marks the FUTURE only once in a sentence. So the choice is between PRESENT and PAST.
Usually — but not always — this means a choice between PRESENT PROGRESSIVE (e.g. is sleeping) and PAST PROGRESSIVE (e.g. was sleeping).

Don't make a noise may refer to all the time or in the future. In either case it must be while your father is sleeping.

You'd use was sleeping for something that was happening in the PAST. For exampleHe made a noise while his father was sleeping.

While your father sleeping is ungrammatical.
If you have a SUBJECT, then you must use a FINITE VERB — in this example is sleeping or was sleeping.

It's possible to use while sleeping but only if the SUBJECT is understood and unstated. For example:My father snores while sleeping. My father used to snore while sleeping.